Magnet (unidirectional): demagnetization curve (HcB, Br) + knee

Presentation

This model (Nonlinear magnet described by H_cB and B_r module, plus knee adjustment) defines a nonlinear B(H) dependence. Non-linearity is considered in the direction of magnetization whereas the model's behavior is linear in the transversal directions.

This magnet model is noted as unidirectional because the mathematical model and the direction of magnetization are dissociated (About orientation of magnets). The mathematical model defines the demagnetization curve, while the direction of magnetization is defined by the orientation in the region (Orient materials in massive regions: volume (3D) / face (2D)).

Mathematical model

The mathematical formula used in Flux for the demagnetization curve is:

with

where:

• μ₀ is the permeability of vacuum, μ₀ = 4 π 10^-7 H/m
• μ_r is the relative permeability of the material (for H = H_cB)
• H_cB is the normal coercivity (A/m)
• a is the knee adjustment coefficient (a > 0 and a < > 1), enabling to adjust the shape of the curve "knee" for a better approximation of the experimental curve. The smaller the coefficient, the sharper the knee is.
• J'_s is computed by bisection method from B_r, H_cB and μ_r, knowing that

The shape of the B(H) dependence in the direction of magnetization is given in the figure below:

In transversal directions one can write:

where μ_r┴ is the transversal relative permeability.

Direction of magnetization

The various possibilities provided to the user are the same ones as those presented in § Magnet (unidirectional): linear approximation.